Vertigo Map for MRI Occupational Safety

• Vertigo Map is a systematic tool that defines spatial risk zones around clinical 3T MRI scanners by quantifying magnetic field gradients and induced electric fields.
• It utilizes high-resolution 3D static magnetic field measurements with rigorous calibration and uncertainty quantification to model field behaviors accurately.
• The approach integrates gradient thresholds and induced-field parameters into a risk index that informs operational safety guidelines and staff training protocols.

A Vertigo Map systematically quantifies and visualizes the spatial regions around a clinical 3T MRI scanner where staff movement may elicit vestibular symptoms, including vertigo, by combining high-resolution three-dimensional measurements of the static magnetic field (SMF), mathematical field modeling, gradient analysis, and induced electric-field calculation. The resulting map supports institutional risk management, occupational safety, and operator training by objectively indexing local vertigo risk as a function of both spatial field gradients and body movement, with explicit thresholds defined by international guidance and peer-reviewed literature (Girardello et al., 6 Aug 2025).

1. Measurement Protocol and Uncertainty Quantification

Comprehensive mapping of the fringe magnetic field requires precision instrumentation and rigorous calibration. The protocol specifies the Narda HP-01 magnetometer, offering 100 nT resolution up to 50 mT and 100 μT above, with 1% DC accuracy. Calibration is performed at the isocentre (reference 3 T field, tolerance ±1 mT), and axis orthogonality is verified by rotating the probe in a controlled environment. Zero-offset and scale factors are logged per the manufacturer’s “exp” accuracy guidance.

Spatial data is sampled on three xz planes parallel to the floor, corresponding to anthropometric landmarks—y = 0.95 m, 1.38 m, and 1.60 m—to represent the typical heights of operator genitals, heart, and head. On each plane, measurements are taken on a uniform 0.10 m grid over 0 ≤ x ≤ 0.75 m and 0 ≤ z ≤ 1.15 m, with a total of 288 points (after discarding data inside the bore, 252 remain).

Uncertainty analysis accounts for instrumental error (σ_exp = 1% B), negligible positioning error (±1 mm), fit residuals (σ_fit), and interpolation errors" derived from both 2D and 3D procedures. The aggregate uncertainty is estimated via quadrature:

$$\sigma_{\text{tot}} = \sqrt{\sigma_{\text{exp}}^2 + \sigma_{\text{fit}}^2 + \sigma_{\text{interp,plane}}^2 + \sigma_{\text{interp,3D}}^2}$$

with σ_tot ≤ 5.6% in fully interpolated zones, and ≤ 10% as the upper acceptable bound for occupational risk mapping (Girardello et al., 6 Aug 2025).

2. Field Modeling, Fitting, and Interpolation

Field values $|B|$, $B_x$, $B_y$, and $B_z$ are fitted on each plane using a parametric basis of nonlinear exponentials and low-order polynomials (typically 4–6 parameters per component). Example fitting relationships for field magnitude and axial component are:

$$B_0(x,z;y_0) = p_1\,e^{-p_2x} + p_3\,x\,e^{-p_4z} + p_5$$

$$B_z(x,z;y_0) = q_1\,z\,\exp(-q_2\sqrt{x^2+z^2}) + q_3\,\exp(-q_4x^2) + q_5$$

Best-fit parameters $p_i$, $q_i$ are determined by least-squares minimization (χ²_red ≈ 1) and alternative parameterizations may be substituted if they yield superior residual statistics. The paper exploits geometric symmetry to extend fitted data into all four quadrants (with axis mirroring and component inversion) before applying natural-neighbor interpolation to the outer measurement zones.

A full three-dimensional grid (1 cm³ voxels) is constructed by interpolating across multiple planes, propagating uncertainties at each voxel as specified above.

3. Gradient Analysis and Vertigo Thresholds

The spatial gradient of the mapped SMF, defined as

$$\nabla B(x,y,z) = \left(\frac{\partial B}{\partial x}, \frac{\partial B}{\partial y}, \frac{\partial B}{\partial z}\right)$$

is calculated either from the analytic fit or via central finite differences on the voxel grid. Literature and ICNIRP guidelines demarcate the primary hazard boundary at

$$|\nabla B| > G_{\text{vertigo}} \approx 2.0\,\mathrm{T/m}$$

where typical walking speeds (~1 m/s) can provoke vertigo and other physiological symptoms. Some studies observe symptom onset at gradients as low as 1 T/m. The protocol conservatively adopts $G_{\text{vertigo}} = 2$ T/m as the onset threshold (Girardello et al., 6 Aug 2025).

4. Induced Electric Field Modeling Due to Motion

The mechanical motion of body tissues in the fringe field induces secondary electric fields, calculated for two principal situations:

• Linear translation:

$$\mathbf{E}(\mathbf{r}) = \mathbf{v} \times \mathbf{B}(\mathbf{r})$$

Maximal magnitude $E \approx v B$ for orthogonal motion.

• Rotational movement (e.g., head/torso turns):

$$E_\theta(r) \approx -r\,\frac{dB}{dt} = -r\,(\nabla B)\cdot(\boldsymbol{\omega} \times \mathbf{r})$$

In simplified form, for rotation at angular speed $\omega$ and radius $r$, $|E_\theta|\approx r |\nabla B| |\mathbf{v}|$.

Typical parameters:

• Slow walk $v \approx 0.5$ m/s, $B$ up to 1 T $\Rightarrow E \approx 0.5$ V/m.
• Rotation $\omega \approx 0.52$ rad/s (30°/s), $r \approx 0.15$ m, $\nabla B \approx 2$ T/m $\Rightarrow E_\theta \approx 0.15$ V/m.

5. Vertigo-Risk Index Definition and Mapping

The protocol formalizes a local dimensionless vertigo risk index $R(x,y,z)$, which combines normalized spatial gradient and induced field criteria:

$$R(x,y,z) = w_g\,\frac{|\nabla B(x,y,z)|}{G_{\text{vertigo}}} + w_E\,\frac{|E(x,y,z)|}{E_{\text{vertigo}}}$$

with $G_{\text{vertigo}} = 2.0$ T/m, $E_{\text{vertigo}} = 0.5$ V/m (based on recent dizziness thresholds), and typically $w_g = w_E = 0.5$.

Risk-index interpretation:

• $R < 1$: Low vertigo risk
• $1 \leq R < 2$: Moderate risk (caution required)
• $R \geq 2$: High risk (avoid rapid movement)

Mapping results are visualized as 2D projections or 3D volumes—using a traffic-light color scheme (green/yellow/red) corresponding to regions of low/moderate/high risk, with overlays of isogauss contours (e.g., $|B|=0.5$ mT, 3 mT) to reference device/implant safety boundaries.

6. Representative Calculation and Movement Guidelines

A sample calculation at $y = 1.38$ m, $x = 0.30$ m, $z = 0.30$ m yields $B \approx 0.6$ T, $B_z \approx 0.05$ T, $\partial B/\partial x \approx 1.8$ T/m, $\partial B/\partial z \approx 1.2$ T/m ($|\nabla B| \approx 2.16$ T/m). For normal movement at $v=0.5$ m/s,

$$E = v B = 0.5 \times 0.6 = 0.30\,\text{V/m}, \quad R = 0.5 \cdot \frac{2.16}{2.0} + 0.5 \cdot \frac{0.30}{0.5} = 0.54 + 0.30 = 0.84 < 1$$

thus, classified “low risk.”

Movement recommendations derived from the risk map:

• Red zones ($R>2$): Restrict speed to $v \leq 0.1$ m/s, prohibit rapid movement.
• Yellow zones ($1 < R < 2$): Limit to $v \leq 0.3$ m/s, avoid abrupt bodily or head turns.
• Green zones ($R < 1$): Standard walking $v \leq 0.6$ m/s acceptable.
• Staff training should utilize digital tools combining gradient maps with colored overlays that dynamically indicate safe/unsafe movement regimes.
• In high-gradient areas, slow, deliberate head turns are advised, and brisk directional changes should be postponed until moving into a lower gradient region.

7. Occupational Safety and Operational Significance

The vertigo map offers a quantitative methodology to guide spatially-optimized operator movement in the MRI suite, minimizing inadvertent exposure to hazardous gradients and maximally induced fields. Its integration into digital simulation tools enhances risk assessment and staff protocol development at institutional level. Overlaying vertigo-risk zoning with device isogauss contours enables unified education on MRI field hazards, appropriate movement speeds, and best practices for mitigating acute neurophysiological symptoms. The axial component mapping, in particular, provides essential input for accurate modeling of rotationally induced fields, which are relevant for head and torso movements (Girardello et al., 6 Aug 2025).

A plausible implication is that future expansions of vertigo mapping may incorporate individual subject sensitivity and personalized movement advisories, as well as dynamic temporal modeling for emergent MRI scanner platforms with even stronger or more complex field geometries.